Lending Mortage Analysis
Exploratory Data Analysis
Marjorie Blanco, Joe Thompson, Haodi Tu
The data set contains 1989 records. The overall descriptive statistics:
## Married Meet credit history guidelines
## No : 678 0 : 171
## Unknown: 3 1 :1816
## Yes :1308 666: 2
##
##
##
## Other obligations as a percent of total income non-Hispanic Black
## Min. : 0.00 No :1792
## 1st Qu.:28.00 Yes: 197
## Median :33.00
## Mean :32.39
## 3rd Qu.:37.00
## Max. :95.00
## Hispanic Male Mortgage loan approved
## No :1878 No : 369 No : 244
## Yes: 111 Unknown: 15 Yes:1745
## Yes :1605
##
##
##
## Loan amount/purchase price Race
## Min. : 2.105 Hispanic : 111
## 1st Qu.: 70.000 non-Hispanic Black: 197
## Median : 80.000 non-Hispanic White:1681
## Mean : 77.064
## 3rd Qu.: 89.894
## Max. :257.143Descriptive statistics by Race:
## $Hispanic
## MARRIED GDLIN OBRAT MALE APPROVE
## No :31 0 :16 Min. :14.60 No :22 No :26
## Unknown: 1 1 :95 1st Qu.:29.00 Unknown: 2 Yes:85
## Yes :79 666: 0 Median :33.00 Yes :87
## Mean :33.46
## 3rd Qu.:38.45
## Max. :62.00
## LOANPRC RACE
## Min. : 39.39 Hispanic :111
## 1st Qu.: 80.00 non-Hispanic Black: 0
## Median : 89.39 non-Hispanic White: 0
## Mean : 85.17
## 3rd Qu.: 90.42
## Max. :162.63
##
## $`non-Hispanic Black`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 76 0 : 53 Min. : 5.60 No : 51 No : 64
## Unknown: 0 1 :144 1st Qu.:31.00 Unknown: 2 Yes:133
## Yes :121 666: 0 Median :35.00 Yes :144
## Mean :34.94
## 3rd Qu.:38.90
## Max. :63.00
## LOANPRC RACE
## Min. : 28.99 Hispanic : 0
## 1st Qu.: 80.00 non-Hispanic Black:197
## Median : 87.02 non-Hispanic White: 0
## Mean : 83.97
## 3rd Qu.: 90.24
## Max. :255.52
##
## $`non-Hispanic White`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 571 0 : 102 Min. : 0.00 No : 296 No : 154
## Unknown: 2 1 :1577 1st Qu.:27.60 Unknown: 11 Yes:1527
## Yes :1108 666: 2 Median :32.50 Yes :1374
## Mean :32.02
## 3rd Qu.:36.50
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 0
## 1st Qu.: 68.182 non-Hispanic Black: 0
## Median : 79.888 non-Hispanic White:1681
## Mean : 75.719
## 3rd Qu.: 89.623
## Max. :257.143
Descriptive statistics by Marital Status:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :678 0 : 64 Min. : 4.00 No :252 No :102
## Unknown: 0 1 :614 1st Qu.:28.00 Unknown: 7 Yes:576
## Yes : 0 666: 0 Median :33.00 Yes :419
## Mean :32.74
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 31
## 1st Qu.: 72.426 non-Hispanic Black: 76
## Median : 80.000 non-Hispanic White:571
## Mean : 77.967
## 3rd Qu.: 89.978
## Max. :162.626
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE LOANPRC
## No :0 0 :0 Min. :13.0 No :1 No :0 Min. : 86.96
## Unknown:3 1 :3 1st Qu.:23.3 Unknown:0 Yes:3 1st Qu.: 88.62
## Yes :0 666:0 Median :33.6 Yes :2 Median : 90.29
## Mean :27.2 Mean : 98.16
## 3rd Qu.:34.3 3rd Qu.:103.76
## Max. :35.0 Max. :117.24
## RACE
## Hispanic :1
## non-Hispanic Black:0
## non-Hispanic White:2
##
##
##
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 0 0 : 107 Min. : 0.00 No : 116 No : 142
## Unknown: 0 1 :1199 1st Qu.:28.00 Unknown: 8 Yes:1166
## Yes :1308 666: 2 Median :33.00 Yes :1184
## Mean :32.22
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 8.772 Hispanic : 79
## 1st Qu.: 68.857 non-Hispanic Black: 121
## Median : 80.000 non-Hispanic White:1108
## Mean : 76.547
## 3rd Qu.: 89.866
## Max. :257.143Descriptive statistics by Gender:
## $No
## MARRIED GDLIN OBRAT MALE APPROVE
## No :252 0 : 31 Min. : 6.99 No :369 No : 50
## Unknown: 1 1 :338 1st Qu.:28.00 Unknown: 0 Yes:319
## Yes :116 666: 0 Median :33.00 Yes : 0
## Mean :32.64
## 3rd Qu.:37.00
## Max. :83.00
## LOANPRC RACE
## Min. : 11.01 Hispanic : 22
## 1st Qu.: 70.83 non-Hispanic Black: 51
## Median : 80.00 non-Hispanic White:296
## Mean : 77.66
## 3rd Qu.: 90.00
## Max. :255.52
##
## $Unknown
## MARRIED GDLIN OBRAT MALE APPROVE
## No :7 0 : 0 Min. :24.00 No : 0 No : 0
## Unknown:0 1 :15 1st Qu.:29.95 Unknown:15 Yes:15
## Yes :8 666: 0 Median :34.50 Yes : 0
## Mean :33.33
## 3rd Qu.:37.65
## Max. :40.30
## LOANPRC RACE
## Min. :39.39 Hispanic : 2
## 1st Qu.:74.93 non-Hispanic Black: 2
## Median :75.42 non-Hispanic White:11
## Mean :75.59
## 3rd Qu.:80.43
## Max. :92.90
##
## $Yes
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 419 0 : 140 Min. : 0.00 No : 0 No : 194
## Unknown: 2 1 :1463 1st Qu.:28.00 Unknown: 0 Yes:1411
## Yes :1184 666: 2 Median :33.00 Yes :1605
## Mean :32.32
## 3rd Qu.:37.00
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 87
## 1st Qu.: 69.655 non-Hispanic Black: 144
## Median : 80.000 non-Hispanic White:1374
## Mean : 76.942
## 3rd Qu.: 89.881
## Max. :257.143There are 3 records are missing married (MARRIED) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC |
|---|---|---|---|---|---|---|---|---|
| 356 | Unknown | 1 | 35.0 | No | Yes | Yes | Yes | 86.95652 |
| 759 | Unknown | 1 | 33.6 | No | No | Yes | Yes | 90.28571 |
| 1392 | Unknown | 1 | 13.0 | No | No | No | Yes | 117.24140 |
There are 3 records are missing married (GDLIN) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC |
|---|---|---|---|---|---|---|---|---|
| 881 | Yes | 666 | 35 | No | No | Yes | Yes | 75.82939 |
| 1229 | Yes | 666 | 26 | No | No | Yes | Yes | 100.00000 |
There are 15 records are missing gender (MALE) field.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC |
|---|---|---|---|---|---|---|---|---|
| 1 | No | 1 | 34.5 | No | No | Unknown | Yes | 75.42373 |
| 127 | No | 1 | 31.6 | No | No | Unknown | Yes | 80.80000 |
| 286 | Yes | 1 | 37.3 | No | No | Unknown | Yes | 80.05337 |
| 452 | Yes | 1 | 40.1 | Yes | No | Unknown | Yes | 75.00000 |
| 618 | Yes | 1 | 38.5 | No | No | Unknown | Yes | 92.90323 |
| 695 | Yes | 1 | 25.0 | No | No | Unknown | Yes | 64.48276 |
| 762 | Yes | 1 | 27.6 | No | No | Unknown | Yes | 75.55556 |
| 768 | No | 1 | 35.6 | No | No | Unknown | Yes | 64.74397 |
| 833 | Yes | 1 | 24.0 | No | Yes | Unknown | Yes | 79.80769 |
| 979 | No | 1 | 31.7 | No | No | Unknown | Yes | 74.86033 |
| 1040 | No | 1 | 38.0 | Yes | No | Unknown | Yes | 75.38462 |
| 1070 | Yes | 1 | 40.3 | No | Yes | Unknown | Yes | 39.39394 |
| 1092 | Yes | 1 | 29.7 | No | No | Unknown | Yes | 90.10239 |
| 1613 | No | 1 | 30.2 | No | No | Unknown | Yes | 90.00000 |
| 1924 | No | 1 | 35.8 | No | No | Unknown | Yes | 75.32051 |
There are 33 records (98.3408748 %) that have LOANPRC > 100%. There are a total of 1989 records.
| ID | MARRIED | GDLIN | OBRAT | BLACK | HISPAN | MALE | APPROVE | LOANPRC |
|---|---|---|---|---|---|---|---|---|
| 9 | Yes | 1 | 30.7 | No | No | Yes | Yes | 100.3009 |
| 37 | Yes | 1 | 35.0 | No | No | Yes | No | 112.7119 |
| 53 | Yes | 1 | 38.0 | No | No | Yes | Yes | 108.5714 |
| 132 | Yes | 1 | 27.6 | No | No | Yes | Yes | 101.1905 |
| 162 | Yes | 1 | 25.0 | No | No | Yes | Yes | 164.7059 |
| 233 | Yes | 1 | 18.0 | No | No | Yes | Yes | 105.5556 |
| 258 | Yes | 1 | 45.0 | No | No | Yes | No | 220.0000 |
| 262 | Yes | 0 | 56.0 | No | No | Yes | No | 257.1429 |
| 294 | Yes | 1 | 37.0 | No | No | Yes | Yes | 148.8095 |
| 490 | Yes | 1 | 25.0 | Yes | No | Yes | Yes | 120.5480 |
| 544 | Yes | 0 | 52.0 | No | No | Yes | Yes | 117.6471 |
| 560 | Yes | 1 | 33.0 | No | Yes | No | No | 137.9310 |
| 565 | No | 1 | 10.0 | No | No | Yes | Yes | 133.3333 |
| 750 | Yes | 1 | 35.0 | No | No | Yes | No | 147.8261 |
| 793 | Yes | 1 | 37.0 | No | No | Yes | No | 130.0000 |
| 798 | No | 1 | 36.0 | No | No | No | Yes | 147.3684 |
| 841 | No | 1 | 41.2 | No | No | Yes | No | 100.0676 |
| 904 | Yes | 1 | 24.0 | No | No | Yes | Yes | 183.3333 |
| 914 | Yes | 1 | 40.0 | No | Yes | Yes | Yes | 111.4286 |
| 940 | Yes | 1 | 38.0 | No | No | Yes | Yes | 128.9474 |
| 947 | Yes | 1 | 18.0 | Yes | No | Yes | Yes | 100.3521 |
| 963 | Yes | 0 | 41.3 | No | Yes | Yes | No | 109.4118 |
| 1112 | No | 0 | 35.5 | No | Yes | No | No | 162.6263 |
| 1206 | No | 1 | 41.0 | No | No | No | Yes | 125.0000 |
| 1322 | No | 1 | 32.0 | No | No | Yes | Yes | 110.5263 |
| 1392 | Unknown | 1 | 13.0 | No | No | No | Yes | 117.2414 |
| 1394 | Yes | 1 | 37.0 | No | No | Yes | Yes | 114.0845 |
| 1457 | Yes | 1 | 19.0 | No | No | Yes | Yes | 108.0000 |
| 1623 | Yes | 1 | 29.0 | No | No | Yes | Yes | 109.0909 |
| 1632 | Yes | 1 | 36.8 | Yes | No | No | Yes | 255.5248 |
| 1667 | No | 1 | 43.0 | No | No | Yes | Yes | 120.0000 |
| 1683 | No | 1 | 25.0 | No | No | No | Yes | 118.7500 |
| 1759 | No | 1 | 46.0 | No | No | No | Yes | 107.2000 |
## $Hispanic
## MARRIED GDLIN OBRAT MALE APPROVE
## No :30 0 :14 Min. :14.60 No :20 No :23
## Unknown: 1 1 :93 1st Qu.:29.00 Unknown: 2 Yes:84
## Yes :76 666: 0 Median :33.00 Yes :85
## Mean :33.31
## 3rd Qu.:38.10
## Max. :62.00
## LOANPRC RACE
## Min. : 39.39 Hispanic :107
## 1st Qu.: 80.00 non-Hispanic Black: 0
## Median : 88.46 non-Hispanic White: 0
## Mean : 83.48
## 3rd Qu.: 90.23
## Max. :100.00
##
## $`non-Hispanic Black`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 76 0 : 53 Min. : 5.60 No : 50 No : 64
## Unknown: 0 1 :141 1st Qu.:31.00 Unknown: 2 Yes:130
## Yes :118 666: 0 Median :35.00 Yes :142
## Mean :35.07
## 3rd Qu.:38.90
## Max. :63.00
## LOANPRC RACE
## Min. : 28.99 Hispanic : 0
## 1st Qu.: 79.96 non-Hispanic Black:194
## Median : 84.22 non-Hispanic White: 0
## Mean : 82.81
## 3rd Qu.: 90.23
## Max. :100.00
##
## $`non-Hispanic White`
## MARRIED GDLIN OBRAT MALE APPROVE
## No : 563 0 : 100 Min. : 0.00 No : 291 No : 148
## Unknown: 1 1 :1553 1st Qu.:27.65 Unknown: 11 Yes:1507
## Yes :1091 666: 2 Median :32.50 Yes :1353
## Mean :32.00
## 3rd Qu.:36.40
## Max. :95.00
## LOANPRC RACE
## Min. : 2.105 Hispanic : 0
## 1st Qu.: 67.797 non-Hispanic Black: 0
## Median : 79.861 non-Hispanic White:1655
## Mean : 74.832
## 3rd Qu.: 89.237
## Max. :100.000## APPROVE
## RACE No Yes
## Hispanic 26 85
## non-Hispanic Black 64 133
## non-Hispanic White 154 1527
## APPROVE
## MARRIED No Yes
## No 102 576
## Unknown 0 3
## Yes 142 1166
## APPROVE
## MALE No Yes
## No 50 319
## Unknown 0 15
## Yes 194 1411
## , , RACE = Hispanic
##
## APPROVE
## MARRIED No Yes
## No 7 24
## Unknown 0 1
## Yes 19 60
##
## , , RACE = non-Hispanic Black
##
## APPROVE
## MARRIED No Yes
## No 27 49
## Unknown 0 0
## Yes 37 84
##
## , , RACE = non-Hispanic White
##
## APPROVE
## MARRIED No Yes
## No 68 503
## Unknown 0 2
## Yes 86 1022
Data Discription
The data set includes the following variables:
- APPROVE = 1 if mortgage loan was approved, = 0 otherwise
- GDLIN = 1 if credit history meets guidelines, = 0 otherwise
- LOANPRC = loan amount/purchase price
- OBRAT = other obligations as a percent of total income
- MALE = 1 if male, = 0 otherwise
- MARRIED = 1 if married, = 0 otherwise
- BLACK = 1 if black, = 0 otherwise
- HISPAN = 1 if Hispanic, = 0 otherwise
Logistic Regression Full Model
log(p/1-p) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC + b_6 * MARRIED + b_7 * MALE\)
##
## Call:
## glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8933 0.2445 0.3128 0.3742 2.3261
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.381531 0.591656 2.335 0.019542 *
## GDLIN1 3.719269 0.217169 17.126 < 0.0000000000000002 ***
## OBRAT -0.034074 0.010310 -3.305 0.000950 ***
## BLACK1 -0.815693 0.240177 -3.396 0.000683 ***
## HISPAN1 -0.900010 0.310585 -2.898 0.003758 **
## LOANPRC -0.016812 0.005074 -3.313 0.000922 ***
## MARRIED1 0.475742 0.192005 2.478 0.013221 *
## MALE1 -0.053947 0.234573 -0.230 0.818107
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1475.4 on 1968 degrees of freedom
## Residual deviance: 959.4 on 1961 degrees of freedom
## AIC: 975.4
##
## Number of Fisher Scoring iterations: 6For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340739.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0168119.
The log odds of loan approval for applicants that meet credit guidelines increases by 3.719269.
The log odds of loan approval for married applicants increases by 0.4757419.
The log odds of loan approval for Black applicants decreases by 0.8156932.
The log odds of loan approval for Hispanic applicants decreases by 0.9000102.
For example, for a black married male whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the log odds of loan approval is 95.37%
Statistical Tests for Individual Predictors
## Overall
## GDLIN1 17.126161
## OBRAT 3.305071
## BLACK1 3.396220
## HISPAN1 2.897795
## LOANPRC 3.313389
## MARRIED1 2.477753
## MALE1 0.229981## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 293.3054 on 1 and 1961 df: p= < 0.000000000000000222## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 10.9235 on 1 and 1961 df: p= 0.00096664## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 11.53431 on 1 and 1961 df: p= 0.00069686## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 8.397215 on 1 and 1961 df: p= 0.0037997## Wald test for MALE
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 0.05289126 on 1 and 1961 df: p= 0.81813## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 10.97855 on 1 and 1961 df: p= 0.00093849## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = "binomial", data = data1)
## F = 6.13926 on 1 and 1961 df: p= 0.013305## llh llhNull G2 McFadden r2ML
## -479.7016510 -737.7148785 516.0264551 0.3497465 0.2305470
## r2CU
## 0.4372079Logistic Regression Reduced Model 1
log(p/1-p) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC + b_6 * MARRIED\)
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.34239 3.72139 -0.03410 -0.81143 -0.89733
## LOANPRC MARRIED1
## -0.01677 0.46093
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1962 Residual
## Null Deviance: 1475
## Residual Deviance: 959.5 AIC: 973.5## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 294.1283 on 1 and 1962 df: p= < 0.000000000000000222## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.93867 on 1 and 1962 df: p= 0.00095878## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 11.47424 on 1 and 1962 df: p= 0.00071961## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 8.358631 on 1 and 1962 df: p= 0.0038808## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 6.482227 on 1 and 1962 df: p= 0.010972## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
## F = 10.92337 on 1 and 1962 df: p= 0.00096669For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340979.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0167734.
The log odds of loan approval for applicants that meet credit guidelines increase by 3.721387.
The log odds of loan approval for married applicants decreases by 0.4609301.
The log odds of loan approval for non married applicants decreases by NA.
The log odds of loan approval for Black applicants decreases by 0.8114263.
The log odds of loan approval for Hispanic applicants decreases by 0.8973309.
For example, for a black married person whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the log odds of loan approval is 95.42%
CIs using profiled log-likelihood
## 2.5 % 97.5 %
## (Intercept) 0.23664368 2.465735226
## GDLIN1 3.30547346 4.157682544
## OBRAT -0.05434377 -0.013920887
## BLACK1 -1.27292218 -0.332543498
## HISPAN1 -1.48462721 -0.264593691
## LOANPRC -0.02697832 -0.006937324
## MARRIED1 0.10487116 0.815796783CIs using standard errors
## 2.5 % 97.5 %
## (Intercept) 0.23158635 2.453187301
## GDLIN1 3.29609767 4.146676358
## OBRAT -0.05430447 -0.013891283
## BLACK1 -1.28092587 -0.341926697
## HISPAN1 -1.50565235 -0.289009441
## LOANPRC -0.02672039 -0.006826433
## MARRIED1 0.10609951 0.815760700Odds ratios only
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1 LOANPRC
## 3.8281698 41.3216682 0.9664769 0.4442240 0.4076563 0.9833665
## MARRIED1
## 1.5855480Odds ratios and 95% CI
## OR 2.5 % 97.5 %
## (Intercept) 3.8281698 1.2669896 11.7721341
## GDLIN1 41.3216682 27.2614457 63.9232116
## OBRAT 0.9664769 0.9471065 0.9861756
## BLACK1 0.4442240 0.2800122 0.7170975
## HISPAN1 0.4076563 0.2265868 0.7675177
## LOANPRC 0.9833665 0.9733823 0.9930867
## MARRIED1 1.5855480 1.1105675 2.2609765Logistic Regression Reduced Model 2
log(p/1-p) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC\)
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.66805 3.69461 -0.03512 -0.81768 -0.85828
## LOANPRC
## -0.01659
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1963 Residual
## Null Deviance: 1475
## Residual Deviance: 965.9 AIC: 977.9## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
## F = 295.2972 on 1 and 1963 df: p= < 0.000000000000000222## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
## F = 11.55879 on 1 and 1963 df: p= 0.00068779## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
## F = 11.68361 on 1 and 1963 df: p= 0.0006434## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
## F = 7.696649 on 1 and 1963 df: p= 0.0055847## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
## F = 10.76933 on 1 and 1963 df: p= 0.0010501For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0351171.
For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0165852.
The log odds of loan approval for applicants that meet credit guidelines increases by 3.6946116.
The log odds of loan approval for Black applicants decreases by 0.8176845.
The log odds of loan approval for Hispanic applicants decreases by 0.8582767.
For example, for a black person whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the log odds of loan approval is 94.72%
CIs using profiled log-likelihood
## 2.5 % 97.5 %
## (Intercept) 0.59360475 2.764561689
## GDLIN1 3.28231679 4.126731408
## OBRAT -0.05537654 -0.014888611
## BLACK1 -1.27852143 -0.339452086
## HISPAN1 -1.44328269 -0.227316096
## LOANPRC -0.02676923 -0.006824773CIs using standard errors
## 2.5 % 97.5 %
## (Intercept) 0.58607300 2.750024092
## GDLIN1 3.27321875 4.116004514
## OBRAT -0.05536176 -0.014872430
## BLACK1 -1.28654690 -0.348822144
## HISPAN1 -1.46462838 -0.251925037
## LOANPRC -0.02649064 -0.006679743Odds ratios only
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1 LOANPRC
## 5.3018115 40.2299456 0.9654924 0.4414526 0.4238919 0.9835516Odds ratios and 95% CI
## OR 2.5 % 97.5 %
## (Intercept) 5.3018115 1.8105031 15.8720816
## GDLIN1 40.2299456 26.6374146 61.9750205
## OBRAT 0.9654924 0.9461288 0.9852217
## BLACK1 0.4414526 0.2784487 0.7121604
## HISPAN1 0.4238919 0.2361513 0.7966689
## LOANPRC 0.9835516 0.9735859 0.9931985Model comparison
## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1961 959.40
## 2 1962 959.46 -1 -0.0531 0.81770
## 3 1963 965.87 -1 -6.4163 0.01131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 8 -479.70
## 2 7 -479.73 -1 0.0531 0.81770
## 3 6 -482.94 -1 6.4163 0.01131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Probit Regression Full Model
Probit(approve) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC + b_6 * MARRIED + b_7 * MALE\)
##
## Call:
## glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9694 0.2361 0.3119 0.3762 2.2711
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.566210 0.309521 1.829 0.067353 .
## GDLIN1 2.142459 0.121264 17.668 < 0.0000000000000002 ***
## OBRAT -0.016400 0.005344 -3.069 0.002148 **
## BLACK1 -0.425865 0.126958 -3.354 0.000795 ***
## HISPAN1 -0.463475 0.163507 -2.835 0.004588 **
## LOANPRC -0.008409 0.002590 -3.247 0.001166 **
## MARRIED1 0.237894 0.096134 2.475 0.013338 *
## MALE1 -0.033267 0.117944 -0.282 0.777896
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1475.43 on 1968 degrees of freedom
## Residual deviance: 958.84 on 1961 degrees of freedom
## AIC: 974.84
##
## Number of Fisher Scoring iterations: 6For every one unit change in OBRAT, the probit odds of loan approval (versus non loan approval) decreases by 0.0163999.
For every one unit change in LOANPRC, the probit odds of loan approval (versus non loan approval) decreases by 0.0084095.
The probit odds of loan approval for applicants that meet credit guidelines increases by 2.1424592.
The probit odds of loan approval for married applicants increases by 0.2378937.
The probit odds of loan approval for Black applicants decreases by 0.4258647.
The probit odds of loan approval for Hispanic applicants decreases by 0.4634752.
For example, for a black married male whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the probit odds of loan approval is 95.02%
Statistical Tests for Individual Predictors
## Wald test for GDLIN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 312.1492 on 1 and 1961 df: p= < 0.000000000000000222## Wald test for OBRAT
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 9.41885 on 1 and 1961 df: p= 0.0021771## Wald test for BLACK
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 11.25188 on 1 and 1961 df: p= 0.00081057## Wald test for HISPAN
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 8.034928 on 1 and 1961 df: p= 0.0046354## Wald test for MALE
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 0.0795587 on 1 and 1961 df: p= 0.77793## Wald test for LOANPRC
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 10.54337 on 1 and 1961 df: p= 0.0011857## Wald test for MARRIED
## in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F = 6.123722 on 1 and 1961 df: p= 0.013422Probit Regression Reduced Model 1
Probit(approve) = $b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC + b_6 * MARRIED $
##
## Call:
## glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = binomial(link = "probit"), data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9709 0.2362 0.3118 0.3775 2.2602
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.541687 0.297610 1.820 0.068740 .
## GDLIN1 2.143873 0.121184 17.691 < 0.0000000000000002 ***
## OBRAT -0.016411 0.005344 -3.071 0.002136 **
## BLACK1 -0.422677 0.126641 -3.338 0.000845 ***
## HISPAN1 -0.461722 0.163423 -2.825 0.004723 **
## LOANPRC -0.008386 0.002588 -3.240 0.001196 **
## MARRIED1 0.228926 0.090475 2.530 0.011397 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1475.43 on 1968 degrees of freedom
## Residual deviance: 958.92 on 1962 degrees of freedom
## AIC: 972.92
##
## Number of Fisher Scoring iterations: 6## Overall
## GDLIN1 17.691026
## OBRAT 3.070619
## BLACK1 3.337594
## HISPAN1 2.825314
## LOANPRC 3.239942
## MARRIED1 2.530275## llh llhNull G2 McFadden r2ML
## -479.4603569 -737.7148785 516.5090432 0.3500736 0.2307356
## r2CU
## 0.4375655For every one unit change in OBRAT, the probit odds of loan approval (versus non loan approval) decreases by 0.0164109.
For every one unit change in LOANPRC, the probit odds of loan approval (versus non loan approval) decreases by 0.0083864.
The probit odds of loan approval for applicants that meet credit guidelines increases by 2.1438732.
The probit odds of loan approval for married applicants increases by 0.2289263.
The probit odds of loan approval for Black applicants decreases by 0.4226766.
The probit odds of loan approval for Hispanic applicants decreases by 0.4617224.
For example, for a black married person whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the probit odds of loan approval is 95.09%
Probit Regression Reduced Model 2
Probit(approve) = $b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * LOANPRC $
##
## Call:
## glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = binomial(link = "probit"), data = data1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8976 0.2466 0.3190 0.3719 2.2140
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.708006 0.290189 2.440 0.014695 *
## GDLIN1 2.135031 0.120676 17.692 < 0.0000000000000002 ***
## OBRAT -0.017003 0.005340 -3.184 0.001453 **
## BLACK1 -0.426583 0.126242 -3.379 0.000727 ***
## HISPAN1 -0.438093 0.163021 -2.687 0.007202 **
## LOANPRC -0.008356 0.002573 -3.248 0.001163 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1475.43 on 1968 degrees of freedom
## Residual deviance: 965.27 on 1963 degrees of freedom
## AIC: 977.27
##
## Number of Fisher Scoring iterations: 5## Overall
## GDLIN1 17.692269
## OBRAT 3.183979
## BLACK1 3.379077
## HISPAN1 2.687345
## LOANPRC 3.247739## llh llhNull G2 McFadden r2ML
## -482.6350057 -737.7148785 510.1597458 0.3457703 0.2282510
## r2CU
## 0.4328537For every one unit change in OBRAT, the probit odds of loan approval (versus non loan approval) decreases by 0.017003.
For every one unit change in LOANPRC, the probit odds of loan approval (versus non loan approval) decreases by 0.0083562.
The probit odds of loan approval for applicants that meet credit guidelines increases by 2.1350313.
The probit odds of loan approval for Black applicants decreases by 0.4265831.
The probit odds of loan approval for Hispanic applicants decreases by 0.4380932.
For example, for a black person whose credit history meets guidline (GDLIN = 1), loan amount price is 100 (LOANPRC = 100) and other obligations as a percent of total income is none (OBRAT = 0), the probit odds of loan approval is 94.3%
Model comparison
## Analysis of Deviance Table
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1961 958.84
## 2 1962 958.92 -1 -0.0799 0.77742
## 3 1963 965.27 -1 -6.3493 0.01174 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Likelihood ratio test
##
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED +
## MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 8 -479.42
## 2 7 -479.46 -1 0.0799 0.77742
## 3 6 -482.64 -1 6.3493 0.01174 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Log Prediction
Logit Model 1
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.34239 3.72139 -0.03410 -0.81143 -0.89733
## LOANPRC MARRIED1
## -0.01677 0.46093
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1962 Residual
## Null Deviance: 1475
## Residual Deviance: 959.5 AIC: 973.5| GDLIN | OBRAT | BLACK | HISPAN | MARRIED | LOANPRC | fit | PredictedProb |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 77.06418 | -0.7616686 | 0.3182841 |
| 0 | 1 | 1 | 0 | 0 | 77.06418 | -0.7957664 | 0.3109318 |
| 0 | 2 | 1 | 0 | 0 | 77.06418 | -0.8298643 | 0.3036738 |
| 0 | 3 | 1 | 0 | 0 | 77.06418 | -0.8639622 | 0.2965122 |
| 0 | 4 | 1 | 0 | 0 | 77.06418 | -0.8980601 | 0.2894493 |
| 0 | 5 | 1 | 0 | 0 | 77.06418 | -0.9321579 | 0.2824871 |
| GDLIN | OBRAT | BLACK | HISPAN | MARRIED | LOANPRC | fit | PredictedProb |
|---|---|---|---|---|---|---|---|
| 0 | 32.38382 | 1 | 0 | 0 | 2.105000 | -0.6085669 | 0.3523862 |
| 0 | 32.38382 | 1 | 0 | 0 | 4.681141 | -0.6517776 | 0.3425891 |
| 0 | 32.38382 | 1 | 0 | 0 | 7.257283 | -0.6949883 | 0.3329243 |
| 0 | 32.38382 | 1 | 0 | 0 | 9.833424 | -0.7381990 | 0.3233981 |
| 0 | 32.38382 | 1 | 0 | 0 | 12.409566 | -0.7814096 | 0.3140162 |
| 0 | 32.38382 | 1 | 0 | 0 | 14.985707 | -0.8246203 | 0.3047838 |
Logit Model 2
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = "binomial", data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 1.66805 3.69461 -0.03512 -0.81768 -0.85828
## LOANPRC
## -0.01659
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1963 Residual
## Null Deviance: 1475
## Residual Deviance: 965.9 AIC: 977.9| GDLIN | OBRAT | BLACK | HISPAN | LOANPRC | fit | PredictedProb |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 77.06418 | -0.4277603 | 0.3946613 |
| 0 | 1 | 1 | 0 | 77.06418 | -0.4628774 | 0.3863034 |
| 0 | 2 | 1 | 0 | 77.06418 | -0.4979945 | 0.3780121 |
| 0 | 3 | 1 | 0 | 77.06418 | -0.5331116 | 0.3697914 |
| 0 | 4 | 1 | 0 | 77.06418 | -0.5682287 | 0.3616456 |
| 0 | 5 | 1 | 0 | 77.06418 | -0.6033458 | 0.3535786 |
| GDLIN | OBRAT | BLACK | HISPAN | LOANPRC | fit | PredictedProb |
|---|---|---|---|---|---|---|
| 0 | 32.38382 | 1 | 0 | 2.105000 | -0.3217734 | 0.4202436 |
| 0 | 32.38382 | 1 | 0 | 4.681141 | -0.3644992 | 0.4098709 |
| 0 | 32.38382 | 1 | 0 | 7.257283 | -0.4072250 | 0.3995777 |
| 0 | 32.38382 | 1 | 0 | 9.833424 | -0.4499508 | 0.3893725 |
| 0 | 32.38382 | 1 | 0 | 12.409566 | -0.4926766 | 0.3792632 |
| 0 | 32.38382 | 1 | 0 | 14.985707 | -0.5354024 | 0.3692578 |
Probit Prediction
Probit Model 1
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC +
## MARRIED, family = binomial(link = "probit"), data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.541687 2.143873 -0.016411 -0.422677 -0.461722
## LOANPRC MARRIED1
## -0.008386 0.228926
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1962 Residual
## Null Deviance: 1475
## Residual Deviance: 958.9 AIC: 972.9| GDLIN | OBRAT | BLACK | HISPAN | MARRIED | LOANPRC | fit | se.fit |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 77.06418 | 0.2989992 | 0.0861630 |
| 0 | 1 | 1 | 0 | 0 | 77.06418 | 0.2933267 | 0.0839904 |
| 0 | 2 | 1 | 0 | 0 | 77.06418 | 0.2877046 | 0.0818437 |
| 0 | 3 | 1 | 0 | 0 | 77.06418 | 0.2821340 | 0.0797245 |
| 0 | 4 | 1 | 0 | 0 | 77.06418 | 0.2766158 | 0.0776346 |
| 0 | 5 | 1 | 0 | 0 | 77.06418 | 0.2711510 | 0.0755755 |
| GDLIN | OBRAT | BLACK | HISPAN | MARRIED | LOANPRC |
|---|---|---|---|---|---|
| 0 | 32.38382 | 1 | 0 | 0 | 2.105000 |
| 0 | 32.38382 | 1 | 0 | 0 | 4.681141 |
| 0 | 32.38382 | 1 | 0 | 0 | 7.257283 |
| 0 | 32.38382 | 1 | 0 | 0 | 9.833424 |
| 0 | 32.38382 | 1 | 0 | 0 | 12.409566 |
| 0 | 32.38382 | 1 | 0 | 0 | 14.985707 |
Probit Model 2
##
## Call: glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC,
## family = binomial(link = "probit"), data = data1)
##
## Coefficients:
## (Intercept) GDLIN1 OBRAT BLACK1 HISPAN1
## 0.708006 2.135031 -0.017003 -0.426583 -0.438093
## LOANPRC
## -0.008356
##
## Degrees of Freedom: 1968 Total (i.e. Null); 1963 Residual
## Null Deviance: 1475
## Residual Deviance: 965.3 AIC: 977.3| GDLIN | OBRAT | BLACK | HISPAN | LOANPRC | fit |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 77.06418 | 0.3584733 |
| 0 | 1 | 1 | 0 | 77.06418 | 0.3521414 |
| 0 | 2 | 1 | 0 | 77.06418 | 0.3458502 |
| 0 | 3 | 1 | 0 | 77.06418 | 0.3396013 |
| 0 | 4 | 1 | 0 | 77.06418 | 0.3333962 |
| 0 | 5 | 1 | 0 | 77.06418 | 0.3272363 |
| GDLIN | OBRAT | BLACK | HISPAN | LOANPRC | fit |
|---|---|---|---|---|---|
| 0 | 32.38382 | 1 | 0 | 2.105000 | 0.3871373 |
| 0 | 32.38382 | 1 | 0 | 4.681141 | 0.3789214 |
| 0 | 32.38382 | 1 | 0 | 7.257283 | 0.3707598 |
| 0 | 32.38382 | 1 | 0 | 9.833424 | 0.3626560 |
| 0 | 32.38382 | 1 | 0 | 12.409566 | 0.3546132 |
| 0 | 32.38382 | 1 | 0 | 14.985707 | 0.3466347 |
